SCO C8: Students will be expected to demonstrate an understanding that the multiplicative relationship between numerators and denominators is constant for equivalent fractions.

Introductory Activity 1: Make a table with the headings: ‘Numerator’ and below it ‘Denominator’. Display or show the equivalent fractions for ½ in this table. Examine the numbers in the table to find relationships between ½ and its equivalent fractions. Can you multiply the numerator and denominator by any factor and make another fraction that would be in this table? Can you predict the numerator if the denominator is 48? Will there be a denominator of 47 in this table? What will the denominator be if the numerator is 16?

Introductory Activity 2: Fold a sheet of paper to show thirds and then unfold the sheets. Shade in two-thirds. Now fold the sheets in the other direction and unfold. How many sections have you created? How does this number of sections compare to the 3 you had in the beginning? How many of these 6 sections are shaded? How does this number compare to the 2 you had shaded earlier? Begin a table.

Introductory Activity 2 continued: Now fold the sheets in half again. What happened to the 3 sections you started with? How many are now shaded? Record this fraction in your table. Predict what would happen if you folded the paper again and write the new fraction in your table. Notice the multiplicative comparison between the numerators and denominators of the equivalent fractions that describe the fractional parts which are shaded.

Student Activities C8.1: Make a table of equivalent fractions for ¾. C8.2: Use paper folding to show that 2- eighths is equivalent to 1-fourth. C8.3: Fill in the missing numbers to create a table of equivalent fractions. Numerator?23?5 Denominator?812??

Student Activities C8.4: Place the numbers in the correct spots in the two tables below. Numerator1X3X Denominator48X16 Numerator2X1020 DenominatorX10XX

Student Activities C8.5: Explain why 2 ½ divided by 5 is another name for ½ and 2/4. C8.6: Examine the table below and identify or give the multiplicative relationship between the numerators and denominators of pairs of fractions in the table. Numerator Denominator

Student Activities C8.7: What do we mean by ‘congruent rectangles’? Shade 3-fourths of each of the eight congruent rectangles given to you in the same way. Leave one of these rectangles showing the 3- fourths but subdivide the other seven rectangles in different ways to show seven different fractions that are equivalent to 3-fourths. Place your equivalent fractions in a table. Write about the relationships between the fractions that you see. Numerator Denominator